Local Eigenvalue Density for General MANOVA Matrices
نویسندگان
چکیده
منابع مشابه
Local Eigenvalue Density for General MANOVA Matrices
We consider random n× n matrices of the form (XX∗ + Y Y ∗)− 1 2 Y Y ∗ (XX∗ + Y Y ∗)− 1 2 , where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spe...
متن کاملUniversality of Local Eigenvalue Statistics for Some Sample Covariance Matrices
Abstract We consider random, complex sample covariance matrices 1 N X ∗X , where X is a p×N random matrix with i.i.d. entries of distribution μ. It has been conjectured that both the distribution of the distance between nearest neighbor eigenvalues in the bulk and that of the smallest eigenvalues become, in the limit N → ∞, p N → 1, the same as that identified for a complex Gaussian distributio...
متن کاملEigenvalue density of correlated complex random Wishart matrices.
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M dagger M where M is a complex matrix drawn from a normalized distribution P(M) approximately exp(-Tr [AMB M dagger]) with A and B positive definite (square) matrices of arbitrary dimensions. Such so-called correlated Wishart matrices occur in many fields ranging from information theo...
متن کاملThe Beta-MANOVA Ensemble with General Covariance
We find the joint generalized singular value distribution and largest generalized singular value distributions of the β-MANOVA ensemble with positive diagonal covariance, which is general. This has been done for the continuous β > 0 case for identity covariance (in eigenvalue form), and by setting the covariance to I in our model we get another version. For the diagonal covariance case, it has ...
متن کاملAlmost-Hermitian Random Matrices: Eigenvalue Density in the Complex Plane
We consider an ensemble of large non-Hermitian random matrices of the form Ĥ + iÂs, where Ĥ and Âs are Hermitian statistically independent random N × N matrices. We demonstrate the existence of a new nontrivial regime of weak non-Hermiticity characterized by the condition that the average of NTrÂs is of the same order as that of TrĤ 2 when N → ∞. We find explicitly the density of complex eigenv...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2013
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-013-0807-8